Polytope of Type {348,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {348,2}*1392
if this polytope has a name.
Group : SmallGroup(1392,171)
Rank : 3
Schlafli Type : {348,2}
Number of vertices, edges, etc : 348, 348, 2
Order of s₀s₁s₂ : 348
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {174,2}*696
   3-fold quotients : {116,2}*464
   4-fold quotients : {87,2}*348
   6-fold quotients : {58,2}*232
   12-fold quotients : {29,2}*116
   29-fold quotients : {12,2}*48
   58-fold quotients : {6,2}*24
   87-fold quotients : {4,2}*16
   116-fold quotients : {3,2}*12
   174-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)
( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30, 59)( 31, 87)
( 32, 86)( 33, 85)( 34, 84)( 35, 83)( 36, 82)( 37, 81)( 38, 80)( 39, 79)
( 40, 78)( 41, 77)( 42, 76)( 43, 75)( 44, 74)( 45, 73)( 46, 72)( 47, 71)
( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)
( 56, 62)( 57, 61)( 58, 60)( 89,116)( 90,115)( 91,114)( 92,113)( 93,112)
( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)(101,104)
(102,103)(117,146)(118,174)(119,173)(120,172)(121,171)(122,170)(123,169)
(124,168)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)(131,161)
(132,160)(133,159)(134,158)(135,157)(136,156)(137,155)(138,154)(139,153)
(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)(175,262)(176,290)
(177,289)(178,288)(179,287)(180,286)(181,285)(182,284)(183,283)(184,282)
(185,281)(186,280)(187,279)(188,278)(189,277)(190,276)(191,275)(192,274)
(193,273)(194,272)(195,271)(196,270)(197,269)(198,268)(199,267)(200,266)
(201,265)(202,264)(203,263)(204,320)(205,348)(206,347)(207,346)(208,345)
(209,344)(210,343)(211,342)(212,341)(213,340)(214,339)(215,338)(216,337)
(217,336)(218,335)(219,334)(220,333)(221,332)(222,331)(223,330)(224,329)
(225,328)(226,327)(227,326)(228,325)(229,324)(230,323)(231,322)(232,321)
(233,291)(234,319)(235,318)(236,317)(237,316)(238,315)(239,314)(240,313)
(241,312)(242,311)(243,310)(244,309)(245,308)(246,307)(247,306)(248,305)
(249,304)(250,303)(251,302)(252,301)(253,300)(254,299)(255,298)(256,297)
(257,296)(258,295)(259,294)(260,293)(261,292);;
s1 := (  1,205)(  2,204)(  3,232)(  4,231)(  5,230)(  6,229)(  7,228)(  8,227)
(  9,226)( 10,225)( 11,224)( 12,223)( 13,222)( 14,221)( 15,220)( 16,219)
( 17,218)( 18,217)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)( 24,211)
( 25,210)( 26,209)( 27,208)( 28,207)( 29,206)( 30,176)( 31,175)( 32,203)
( 33,202)( 34,201)( 35,200)( 36,199)( 37,198)( 38,197)( 39,196)( 40,195)
( 41,194)( 42,193)( 43,192)( 44,191)( 45,190)( 46,189)( 47,188)( 48,187)
( 49,186)( 50,185)( 51,184)( 52,183)( 53,182)( 54,181)( 55,180)( 56,179)
( 57,178)( 58,177)( 59,234)( 60,233)( 61,261)( 62,260)( 63,259)( 64,258)
( 65,257)( 66,256)( 67,255)( 68,254)( 69,253)( 70,252)( 71,251)( 72,250)
( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,244)( 79,243)( 80,242)
( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)( 88,292)
( 89,291)( 90,319)( 91,318)( 92,317)( 93,316)( 94,315)( 95,314)( 96,313)
( 97,312)( 98,311)( 99,310)(100,309)(101,308)(102,307)(103,306)(104,305)
(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,298)(112,297)
(113,296)(114,295)(115,294)(116,293)(117,263)(118,262)(119,290)(120,289)
(121,288)(122,287)(123,286)(124,285)(125,284)(126,283)(127,282)(128,281)
(129,280)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)(136,273)
(137,272)(138,271)(139,270)(140,269)(141,268)(142,267)(143,266)(144,265)
(145,264)(146,321)(147,320)(148,348)(149,347)(150,346)(151,345)(152,344)
(153,343)(154,342)(155,341)(156,340)(157,339)(158,338)(159,337)(160,336)
(161,335)(162,334)(163,333)(164,332)(165,331)(166,330)(167,329)(168,328)
(169,327)(170,326)(171,325)(172,324)(173,323)(174,322);;
s2 := (349,350);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(350)!(  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)
(  9, 22)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30, 59)
( 31, 87)( 32, 86)( 33, 85)( 34, 84)( 35, 83)( 36, 82)( 37, 81)( 38, 80)
( 39, 79)( 40, 78)( 41, 77)( 42, 76)( 43, 75)( 44, 74)( 45, 73)( 46, 72)
( 47, 71)( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)
( 55, 63)( 56, 62)( 57, 61)( 58, 60)( 89,116)( 90,115)( 91,114)( 92,113)
( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)( 99,106)(100,105)
(101,104)(102,103)(117,146)(118,174)(119,173)(120,172)(121,171)(122,170)
(123,169)(124,168)(125,167)(126,166)(127,165)(128,164)(129,163)(130,162)
(131,161)(132,160)(133,159)(134,158)(135,157)(136,156)(137,155)(138,154)
(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)(175,262)
(176,290)(177,289)(178,288)(179,287)(180,286)(181,285)(182,284)(183,283)
(184,282)(185,281)(186,280)(187,279)(188,278)(189,277)(190,276)(191,275)
(192,274)(193,273)(194,272)(195,271)(196,270)(197,269)(198,268)(199,267)
(200,266)(201,265)(202,264)(203,263)(204,320)(205,348)(206,347)(207,346)
(208,345)(209,344)(210,343)(211,342)(212,341)(213,340)(214,339)(215,338)
(216,337)(217,336)(218,335)(219,334)(220,333)(221,332)(222,331)(223,330)
(224,329)(225,328)(226,327)(227,326)(228,325)(229,324)(230,323)(231,322)
(232,321)(233,291)(234,319)(235,318)(236,317)(237,316)(238,315)(239,314)
(240,313)(241,312)(242,311)(243,310)(244,309)(245,308)(246,307)(247,306)
(248,305)(249,304)(250,303)(251,302)(252,301)(253,300)(254,299)(255,298)
(256,297)(257,296)(258,295)(259,294)(260,293)(261,292);
s1 := Sym(350)!(  1,205)(  2,204)(  3,232)(  4,231)(  5,230)(  6,229)(  7,228)
(  8,227)(  9,226)( 10,225)( 11,224)( 12,223)( 13,222)( 14,221)( 15,220)
( 16,219)( 17,218)( 18,217)( 19,216)( 20,215)( 21,214)( 22,213)( 23,212)
( 24,211)( 25,210)( 26,209)( 27,208)( 28,207)( 29,206)( 30,176)( 31,175)
( 32,203)( 33,202)( 34,201)( 35,200)( 36,199)( 37,198)( 38,197)( 39,196)
( 40,195)( 41,194)( 42,193)( 43,192)( 44,191)( 45,190)( 46,189)( 47,188)
( 48,187)( 49,186)( 50,185)( 51,184)( 52,183)( 53,182)( 54,181)( 55,180)
( 56,179)( 57,178)( 58,177)( 59,234)( 60,233)( 61,261)( 62,260)( 63,259)
( 64,258)( 65,257)( 66,256)( 67,255)( 68,254)( 69,253)( 70,252)( 71,251)
( 72,250)( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,244)( 79,243)
( 80,242)( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)
( 88,292)( 89,291)( 90,319)( 91,318)( 92,317)( 93,316)( 94,315)( 95,314)
( 96,313)( 97,312)( 98,311)( 99,310)(100,309)(101,308)(102,307)(103,306)
(104,305)(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,298)
(112,297)(113,296)(114,295)(115,294)(116,293)(117,263)(118,262)(119,290)
(120,289)(121,288)(122,287)(123,286)(124,285)(125,284)(126,283)(127,282)
(128,281)(129,280)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)
(136,273)(137,272)(138,271)(139,270)(140,269)(141,268)(142,267)(143,266)
(144,265)(145,264)(146,321)(147,320)(148,348)(149,347)(150,346)(151,345)
(152,344)(153,343)(154,342)(155,341)(156,340)(157,339)(158,338)(159,337)
(160,336)(161,335)(162,334)(163,333)(164,332)(165,331)(166,330)(167,329)
(168,328)(169,327)(170,326)(171,325)(172,324)(173,323)(174,322);
s2 := Sym(350)!(349,350);
poly := sub<Sym(350)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope